1. “Basis” risk may arise in a hedging situation if

a) The expiry date of the futures contract and the date on which the hedge is unwound do not coincide.

b) The futures contract used for hedging relates to a commodity that is somewhat different than that being hedged.

c) A disconnect between spot and futures markets causes the failure of the convergence of futures to spot at expiry of the futures contract.

d) All of the above.

2. If changes in spot and futures prices are perfectly correlated over the horizon of a hedge, then

a) The minimum variance hedge ratio is .

b) The variance of cash flows from a hedged position under the minimum-variance hedge ratio is zero.

c) The net cash flow at maturity of the hedge is zero.

d) The standard deviation of spot price changes must equal the standard deviation of futures price changes.

3. If changes in spot and futures prices are uncorrelated, then

a) The minimum variance hedge ratio is zero.

b) Basis risk is zero.

c) Hedging the spot position with futures is effective because the portfolio is well-diversified.

d) The minimum variance hedge requires holding equal amounts of spot and futures.

4. If changes in spot and futures prices have a correlation of , then

a) The hedge ratio is .

b) The variance of cash flows from a hedged position under the minimum-variance hedge ratio is zero.

c) The net cash flow at maturity of the hedge is zero.

d) The standard deviation of spot price changes must equal the negative of the standard deviation of futures price changes.

5. You are hedging a spot position with futures. If the spot asset is more volatile than the corresponding futures, the minimum-variance hedge ratio is

a) Greater than 1.

b) Exactly equal to 1.

c) Less than 1.

d) Indeterminate, given the information available.

6. You are hedging a spot position with futures. If the spot asset is less volatile than the futures, and there is basis risk, which of the following is surely false:

a) The minimum-variance hedge ratio is greater than 1.

b) The minimum-variance hedge ratio is less than or equal to 1.

c) The minimum-variance hedge ratio is negative.

d) The minimum-variance hedge ratio is not equal to 1.

7. The correlation between changes in price of a spot asset and futures asset is 90%. The standard deviation of changes in spot prices is $2, and that of futures prices is $2.50. The hedge ratio that minimizes hedge variance is

a) 0.70

b) 0.72

c) 0.80

d) 0.85

8. The correlation between changes in price of a spot asset and futures asset is 99%. The standard deviation of changes in spot prices is $2, and that of futures prices is $3. What is the standard deviation of a position that is long 5 units of the spot asset and is hedged by shorting 4 units of futures?

a) 1.5

b) 2.0

c) 2.5

d) 3.0

9. The correlation between changes in price of a spot asset and futures asset is 99%. The standard deviation of changes in spot prices is $2, and that of futures prices is $3. What is the standard deviation of a position that is long 5 units of the spot asset and is optimally (i.e., minimum-variance) hedged by using futures?

a) 1.41

b) 1.99

c) 2.52

d) 3.11

10. Using a linear regression of changes in spot asset prices on changes in futures asset prices, the minimum-variance hedge ratio may be obtained

a) As the intercept coefficient in the regression.

b) As the slope coefficient in the regression.

c) As the of the regression.

d) As the square-root of the variance of the residuals from the regression.

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